Fluctuation relation for a L\'evy particle

We study the work fluctuations of a particle subjected to a deterministic drag force plus a random forcing whose statistics is of the L\'evy type. In the stationary regime, the probability density of the work is found to have ``fat'' power-law tails which assign a relatively high probability to large fluctuations compared with the case where the random forcing is Gaussian. These tails lead to a strong violation of existing fluctuation theorems, as the ratio of the probabilities of positive and negative work fluctuations of equal magnitude behaves in a non-monotonic way. Possible experiments that could probe these features are proposed.Comment: 5 pages, 2 figures, RevTeX4; v2: minor corrections and references added; v3: typos corrected, new conclusion, close to published versio

К ВОПРОСУ О РАСШИРЕНИИ ПОКАЗАНИЙ ПРИМЕНЕНИЯ ИММУНОМОДУЛИРУЮЩЕГО ПРЕПАРАТА В ЛЕЧЕНИИ И ПРОФИЛАКТИКЕ ГРИППА И ОСТРЫХ РЕСПИРАТОРНЫХ ИНФЕКЦИЙ У ДЕТЕЙ РАННЕГО ВОЗРАСТА

The data on the safety and effectiveness of the use of the domestic immunomodulating preparation Polyoxidonium® (azoximer bromide) in children are summarized in the following pages. Polyoxidonium has an immunomodulatory (including interferon-inducing), detoxication and anti-inflammatory effect that allows the clinical course of the disease to be quickly alleviated and the natural immune response modulated. The clinical effectiveness of the drug in acute respiratory infections (ARI) in children, including those with allergic anamnesis. Recent studies have proven the effectiveness of the 7-day course of the preparation Polyoxidonium® for the treatment and prevention of ARI and influenza in children, starting at the age of 3 years, as evidenced by a rapid positive dynamics of clinical symptoms and a 2-fold decrease in ARI frequency compared to placebo group at 6 months after the end of therapy.  Обобщены данные о безопасности и эффективности применения отечественного иммуномодулирующего препарата Полиоксидоний®(азоксимера бромид (azoximer bromide) у детей. Полиоксидоний оказывает иммуномодулирующее (в том числе интерферонин-дуцирующее), детоксикационное и противовоспалительное действие, что позволяет быстро облегчать клиническое течение заболевания и модулировать естественный иммунный ответ. Доказана клиническая эффективность препарата при острых респираторных инфекциях (ОРИ) у детей, в том числе с отягощенным аллергоанамнезом. Последние исследования доказали эффективность 7-дневного курсового приема препарата Полиоксидоний® для лечения и профилактики ОРИ и гриппа у детей, начиная с 3-х летнего возраста, о чем свидетельствовала быстрая положительная динамика клинических симптомов и уменьшение частоты ОРИ в 2 раза по сравнению с группой плацебо через 6 мес. после окончания терапии. 

Characteristics of air showers created by extremely high energy gamma-rays

The technique of adjoint cascade equations has been applied to calculate the properties of extremely high energy gamma-rays in the energy range 10^18--10^22 eV with taking into account the LPM effect and interactions of gamma-rays with the geomagnetic field. Such characteristics are analysed as the electron and muon contents at the observation level, the electron cascade curves, the lateral distribution functions of photoproduced muons.Comment: 36 pages, 19 figures, submitted to J.Phys.G: Nucl.Part.Phy

Conductance of 1D quantum wires with anomalous electron-wavefunction localization

We study the statistics of the conductance $g$ through one-dimensional disordered systems where electron wavefunctions decay spatially as $|\psi| \sim \exp (-\lambda r^{\alpha})$ for $0 <\alpha <1$, $\lambda$ being a constant. In contrast to the conventional Anderson localization where $|\psi| \sim \exp (-\lambda r)$ and the conductance statistics is determined by a single parameter: the mean free path, here we show that when the wave function is anomalously localized ($\alpha <1$) the full statistics of the conductance is determined by the average $$ and the power $\alpha$. Our theoretical predictions are verified numerically by using a random hopping tight-binding model at zero energy, where due to the presence of chiral symmetry in the lattice there exists anomalous localization; this case corresponds to the particular value $\alpha =1/2$. To test our theory for other values of $\alpha$, we introduce a statistical model for the random hopping in the tight binding Hamiltonian.Comment: 6 pages, 8 figures. Few changes in the presentation and references updated. Published in PRB, Phys. Rev. B 85, 235450 (2012

Theory of Systematic Computational Error in Free Energy Differences

Systematic inaccuracy is inherent in any computational estimate of a non-linear average, due to the availability of only a finite number of data values, N. Free energy differences (DF) between two states or systems are critically important examples of such averages in physical, chemical and biological settings. Previous work has demonstrated, empirically, that the ``finite-sampling error'' can be very large -- many times kT -- in DF estimates for simple molecular systems. Here, we present a theoretical description of the inaccuracy, including the exact solution of a sample problem, the precise asymptotic behavior in terms of 1/N for large N, the identification of universal law, and numerical illustrations. The theory relies on corrections to the central and other limit theorems, and thus a role is played by stable (Levy) probability distributions.Comment: 5 pages, 4 figure

Levy stable distributions via associated integral transform

We present a method of generation of exact and explicit forms of one-sided, heavy-tailed Levy stable probability distributions g_{\alpha}(x), 0 \leq x < \infty, 0 < \alpha < 1. We demonstrate that the knowledge of one such a distribution g_{\alpha}(x) suffices to obtain exactly g_{\alpha^{p}}(x), p=2, 3,... Similarly, from known g_{\alpha}(x) and g_{\beta}(x), 0 < \alpha, \beta < 1, we obtain g_{\alpha \beta}(x). The method is based on the construction of the integral operator, called Levy transform, which implements the above operations. For \alpha rational, \alpha = l/k with l < k, we reproduce in this manner many of the recently obtained exact results for g_{l/k}(x). This approach can be also recast as an application of the Efros theorem for generalized Laplace convolutions. It relies solely on efficient definite integration.Comment: 12 pages, typos removed, references adde

ЭФФЕКТИВНОСТЬ НАТУРАЛЬНОГО ПРЕПАРАТА В ЛЕЧЕНИИ И ПРОФИЛАКТИКЕ ГРИППА И ДРУГИХ ОСТРЫХ РЕСПИРАТОРНЫХ ЗАБОЛЕВАНИЙ У ДЕТЕЙ

The results of application of the drug of natural origin (Aflubin) with immunomodulating, anti-inflammatory, detoxifying effect in complex treatment of influenza and acute respiratory infections in children are presented. The inclusion of Aflubin in the complex treatment of diseases contributed to reducing the severity and duration of intoxication, reducing the duration of catarrhal phenomena, preventing the development of secondary bacterial complications. Relative simplicity of the drug (drops) at affordable cost, therapeutic and preventive efficacy in all age groups ensure its high compliance. Представлены результаты применения препарата природного происхождения (Афлубин) с иммуномодулирующим, противовоспалительным, дезинтоксикационным действием в комплексном лечении гриппа и острых респираторных инфекций у детей. Включение препарата Афлубин в комплекс лечения заболеваний способствовало уменьшению выраженности и длительности интоксикации, сокращению продолжительности катаральных явлений, предупреждению развития вторичных бактериальных осложнений. Относительная простота применения препарата (капли) при доступной стоимости, лечебная и профилактическая эффективность во всех возрастных группах обеспечивают его высокий комплаенс.

Cooling down Levy flights

Let L(t) be a Levy flights process with a stability index \alpha\in(0,2), and U be an external multi-well potential. A jump-diffusion Z satisfying a stochastic differential equation dZ(t)=-U'(Z(t-))dt+\sigma(t)dL(t) describes an evolution of a Levy particle of an `instant temperature' \sigma(t) in an external force field. The temperature is supposed to decrease polynomially fast, i.e. \sigma(t)\approx t^{-\theta} for some \theta>0. We discover two different cooling regimes. If \theta<1/\alpha (slow cooling), the jump diffusion Z(t) has a non-trivial limiting distribution as t\to \infty, which is concentrated at the potential's local minima. If \theta>1/\alpha (fast cooling) the Levy particle gets trapped in one of the potential wells

Noise-induced escape in an excitable system

We consider the stochastic dynamics of escape in an excitable system, the FitzHugh-Nagumo (FHN) neuronal model, for different classes of excitability. We discuss, first, the threshold structure of the FHN model as an example of a system without a saddle state. We then develop a nonlinear (nonlocal) stability approach based on the theory of large fluctuations, including a finite-noise correction, to describe noise-induced escape in the excitable regime. We show that the threshold structure is revealed via patterns of most probable (optimal) fluctuational paths. The approach allows us to estimate the escape rate and the exit location distribution. We compare the responses of a monostable resonator and monostable integrator to stochastic input signals and to a mixture of periodic and stochastic stimuli. Unlike the commonly used local analysis of the stable state, our nonlocal approach based on optimal paths yields results that are in good agreement with direct numerical simulations of the Langevin equation